Hi, Be under now illusion Basenji's are the smartest in the room and if you can be at least 1/2 a step ahead of them you will be in with a small chance. Your previous experience with your Great Pyrenees will be a good start but rather than having a 50lb lumbering toddler, you with have an impish speed freak and you will have little chance of catching them. They also can jump onto the worktop from stand still so make sure you don't leave any food out. On the best side, she will be the cuddliest, loving snuggle and loyal little girl you could wish for.
Try chopped carrots for treats and train with praise and cuddles. Never chase after her if she runs off as he will think you are playing the game but walk the other way. You may get a lot of negative comments about this but it works for me. I've only highlighted some of the problems I've had with my George and it's taken me 6-7 years working this out and he still gets one over on me now and again. Hopefully your won't have half of these problems and I wish you all the happy days I've had with George.